Student Essay Contest

Hooked on Hyperbolic Planes

2018 Essay Contest: Undergraduate Level Honorable Mention

By: Linnea Rylander, Massachusetts Institute of Technology (Cambridge Massachusetts)

Many people assume that mathematics and the arts don’t mix. Fortunately, Daina Taimina isn’t one of them. Currently a retired adjunct associate professor of mathematics at Cornell University, Taimina has used her artistic prowess to crochet hyperbolic planes and in doing so she has dispelled the assumptions of her counterparts concerning the miscibility of math and art.
But that’s not to say it was easy to defy such stereotypes. Reflecting on the comments of her fourth grade art teacher, Professor Taimina shared, “[He] told me that I might be the best student in math, but I had no artistic eye and my drawing was horrible. I liked to draw and was sad about [this] prejudgment, so I grew up convinced that I was really bad at art.” Taimina relished the pursuit of knowledge from an early age. Growing up in Riga, Latvia, her family lived in a shared apartment. One of the other tenants was a man named Professor Skuja.
“He was my first teacher. He taught me to read at the age of four [and] taught me that the most valuable thing one can possess is knowledge. He said, ‘Everything else can be taken away from you, but what is in your head will always be with you and will help you to survive.’” Based on the sheer breadth of her accomplishments, it is clear that Taimina used her thirst for knowledge to do far more than just survive. She flourished.
By the Spring of 1977, her senior year at the University of Latvia, Taimina was anxiously anticipating graduation. However, there were still a few classes she needed to conclude in order to obtain her degree, one of which was Hyperbolic Geometry. Despite her knack for mathematics, she struggled with this class and ended up loathing it, recalling that “hyperbolic geometry required a little too much imagination for me to make sense of it.” She passed, but hoped to never encounter hyperbolic geometry again. Little did she realize that this very subject would become her life’s work.
After graduating from the University of Latvia with highest distinction, Taimina completed her graduate work in theoretical computer science in 1990. After Latvia regained independence in 1991, she received her doctorate in mathematics from the University of Latvia and subsequently taught at that same university. In 1996, she journeyed to the United States to join the mathematics department at Cornell. Soon enough, Professor Taimina was tasked with teaching hyperbolic geometry during Cornell’s fall semester. In order to prepare for this challenge, she attended a geometry workshop over the summer where a delicate paper model was used to visualize hyperbolic geometry. Taimina recalls, “My fingers itched to touch it, but I was not allowed to touch, because this fragile little thing would be easily destroyed.” There had to be a more durable, tangible way to capture the exponential nature of hyperbolic planes; she set out to find it. During that same workshop, Taimina had an epiphany. The rapid increases reminded her of incrementing in crochet patterns. Inspired, she retrieved her hooks and began constructing a hyperbolic plane that grew in accordance with the exponential equation y=(3/2)x. However, according to Professor Taimina, “This model came out too ruffled, so I figured the exponential growth of the number of stitches should be slowed down more, making the ratio even closer to one.” She pressed on, experimenting with various ratios until she was able to crochet a model that allowed her to demonstrate the unique attributes of lines on hyperbolic surfaces.
Finally, her goal came to fruition. She successfully developed a tactile model of a hyperbolic plane, a feat previously deemed unachievable. In doing so, she improved the accessibility of this once completely theoretical concept. After sharing her work with others, students from across the globe were finally able to experience hyperbolic planes hands-on and achieve an elevated level of understanding. However, while many praised her for this profound achievement, other mathematicians expressed criticism. “There were people who said that I was not serious enough – mathematicians do mathematics not crochet.” These individuals gave into stereotypes and considered mathematics too formal to be accessible by all.
Likewise, others mocked her use of crochet due to the preconceived notion that crochet is “something women do when they have nothing else to do.” But rather than accept the critique and give up on her newfound approach, Taimina’s determination would not let her quit. She faced these stereotypes with resilience and proceeded to convince the editor of The Mathematical Intelligencer to accept her paper concerning the applications of crocheting hyperbolic planes. Since then, she has continued to share her work with the world. Not only did she write a book titled Crocheting Adventures with Hyperbolic Planes (just released in a second edition), she has also given a plethora of talks, been featured in various art shows and museums, been interviewed by mathematicians and crochet enthusiasts alike, and won the esteemed Euler Book Prize in 2012. Furthermore, her use of crochet to model hyperbolic planes has been adopted by The Institute For Figuring and transformed into the Crochet Coral Reef ecological project which involves thousands of participants from across the globe.
In the future, her mathematical creativity will continue to have a ripple effect. Professor Taimina’s contributions to non-euclidean geometry have brought mathematics to a profound level of accessibility, allowing curious minds from an infinite number of backgrounds to push aside stereotypes, embrace the close-knit compatibility of two seemingly discrete fields, and unravel the beauty of mathematics.
About the student:
Linnea is a Computer Science student at the Massachusetts Institute of Technology. She owns her own personal crochet pattern design business and programmed her own website to host her latest creations: . As a Calculus 3 student, it was Professor Daina Taimina’s work that encouraged her to crochet a three-dimensional model (in order to visualize hyperbolic paraboloids) and share it with her classmates. Non-euclidian geometry is quite possibly her favorite aspect of mathematics. Linnea looks forward to further exploring the mathematical applications of crochet.